(i) Write the MATLAB code to find the equation of tangent to the curve yz = 4 -3x at (-2,5). Also visualize them pictorially.

Answer 1

The actual 3dplot of the function: Use something like:

[x y] = meshgrid(-5 : .1 : 5); (format is lowbound, interval, highbound - see how it looks)

z = (4-3x)./y; (note ./ not /)

plot3(x,y,z);

Finding the tangent plane is more a math problem:

Let F(x,y,z) = yz-4+3x find tangent at P₀ = (-2,5,2) (z obtained by plugging in x and y)

The equation of the plane is derived from delF•(r - r₀) where r₀ points to P₀ This is true because the tangent plane is perpendicular to the local normal (delF)

In cartesian coordinates:

F_x(x-x₀) + F_y(y-y₀) + F_z(z-z₀) = 0 where F_i is the partial derivative of F with respect to i at the point.

Once you have that equation you could plot the plane using the same technique with a meshgrid and plot3. If you want to put them on the same graph, type hold on in the workspace before plotting second graph.